Monday, April 06, 2009

Below is Eli's translation from the German of Jörg Zimmerman's take on G&T. The Rabett will excerpt parts of this for a final part in our opus, taking care to desnark. Eli realizes that everyone else is right damn you all, and we have to desnark to put the paper where it belongs.

At the time he wrote this Jörg did not have access to the IJMP paper so there will be some minor differences, different page numbers, etc. which should be allowed for, and that does not detract from the many valid points he makes.

Scientific debate occurs primarily in peer-reviewed journals. The system has been established to save time and resources. In principle, if everything were published, everyone who wanted to play scientist could submit manuscripts to the journals. That would result in publication of a phonebook thick journal every week in every field of which 90% would be useless. Expert reviews should select submissions so that the journals are readable. How well this works depends on how much time the referees take, how carefully they work and how close their own work is to the articles they review. Expert peer review is no guarantee that the work is correct. Over time the value of the work becomes obvious when others build on it, the work is frequently cited by others, whether it stands up to criticism (some papers will be commented on and this can lead to corrections), and how it matches with the work of others (good work can be replicated and the results can be confirmed by other methods). Publication usually requires two (or more) positive evaluations from volunteer referees who are themselves experts in the same field as the submitted manuscript. Normally, the referees are anonymous. In highly specialized areas, there are often only a few qualified specialists and there is a good chance that you can guess from the comments, who the referees were.

The system obviously has its weaknesses. There are negligent referees, there are those that want to wreck havoc on their competitors or wink at their friends and those who are simply overwhelmed. The latter is more likely if the submission is at the outer limits of the journal’s usual focus because the editor will have difficulty choosing competent reviewers. Some reviewers hide behind their anonymity, some fear, perhaps, that they could no longer be independent judges if the review were not anonymous. There will always be a debate about the flaws of peer review, improvements will be proposed, but for all its weaknesses, it is the system that we have and for 90% of submissions it seems to work. Unfortunately, some believe that peer review will ensure that only proper, serious, well-written articles will be published. This expectation is naive. In general, peer review ensures that 50-70% of submitted contributions will be published (more or less, depending on the reputation of the journal) and after peer review most of the articles have some value, especially if the paper is relevant to the reviewer’s own work.

Sometimes peer review fails so badly that you have to slap your head and stand speechless.

(That's Georg Hoffmann who takes on the dreaded Krammbot in the comments at Prima Klima)The fabrication that aspires to be a scientific article

The physicists Gerlich and Tscheuschner have created a fabrication that had circulated for three years previously amidst great fanfare in denialist circles. In all seriousness they claim that they have disproved the greenhouse effect. We should not have to seriously discuss this. It is so obviously wrong that one’s time should not be wasted. There are people who still claim that a perpetual motion machine can be built, that the theories of relativity are wrong or the world was created in six days. These are not the subject of serious scientific discussion and should be eliminated by peer review. Yet, be that what it may, Gerlich and Tscheuschner have found a physics journal to house their contribution. It is the International Journal of Modern Physics, B, not a journal of geophysics, climatology or meteorology but a journal that publishes articles about condensed matter, high temperature superconductors, and statistical and applied physics. To attentive observers this immediately raises red flags that something is seriously wrong. You would not expect editors of such a journal to have much expertise about climate. According to the published rules of the journal all review articles, such as that of Gerlich and Tscheuschner must be invited which is still more concerning.

In spite of all this, this fabrication has been published in a scientific journal so we are obligated to say what is rotten with it. That is not simple to do. The manuscript is unusually long. The electronic edition has 115 pages. To be sure review articles that long have been published, but this submission does not resemble a review article. The stated issue, the greenhouse effect, can be handled in fewer than ten pages. A response to the article by Arthur Smith used nine pages to show that there is a greenhouse effect. If this was really a review of all relevant literature on the greenhouse effect, it could be somewhat longer, but this is exactly what was not done here. Scarcely any of the references deal with the supposed theme of the paper, making the submission a parody of a review article.

Another sign is that the authors mainly talk about “problems” that are not really problems. These are then "resolved", but they were never relevant to the real issue.For example, one of these deals extensively with the contribution of heat conduction. However, the greenhouse effect is an effect of the radiation budget of the earth. Heat conduction in the atmosphere is tiny compared to radiation and convection. It can be neglected and is thus irrelevant.

The work is full of polemics, which should not be found in a scientific publication. In that regard, large sections appear not to be a scientific contribution, but a political comment with technical background. That should also be a warning sign that it is a work without scientific value trying to imitate a journal article. One is driven to presume that the paper is so long to convey the appearance of scientific competence through overcomplicated discussions of irrelevant problems where actual technical expertise is lacking.

The list of references is another sign of this. It includes many books, including textbooks, without page numbers. Therefore one would have to read the entire book to discover where it supports a statement in the article. One can occasionally do this in special circumstances, e.g. if introductory texts are referred to, but even then it is best to use page numbers. As done here, it is not helpful. The books cited are in part works of opinion and political polemics. Many of the references are to polemics or anonymous contributions from the Internet or from the gray literature. In addition, newspaper articles are cited, very unusual in a scientific article. A major proportion of the cited literature has no relation to the greenhouse effect or to questions of radiation balance. Obviously including a discussion of temperature reconstructions of the last 2000 years is not relevant, especially not if it is just used to bash Michael Mann. A number of well known deniers are quoted, so to speak back scratching among comrades. For historical CO2 levels the key citation is to a paper published in a sociology journal by a retired secondary school teacher E. Beck. If such citations are placed on the same level as those of Keeling and other reputable researchers, then it becomes clear that this is not a serious presentation of research on CO2 mixing ratios in the background atmosphere. (At a second look, this reference is not used in the text – it remained there from an earlier version of this work.)

The falsification starts in Section 1, Introduction, which occupies only 9 pages (!) and which is stuffed with irrelevancies. For the greenhouse effect thermal conductivity of CO2 or other gases is unimportant. Further, the IPCC’s basic argument about the greenhouse effect is not, as G & T argue, that there must exist a mysterious consensus, but from the cited literature (see below).

The atmosphere is not a greenhouse

One now comes to section 2. First, in 2.1 the authors entrap us into a long, overcomplicated calculation, to show that the Stefan-Boltzmann Law does not apply, to emission and absorption from molecular vibrational bands. This is true, but is also known, and for the greenhouse effect it is not relevant. The Stefan-Boltzmann law is not used to calculate the greenhouse effect in any except the simplest models. It serves only in simplified models to estimate the magnitude of the greenhouse effect. In Section 2.2, the sun is described as a black radiator at a temperature of about 5780 degree. What a surprise! One would have to refer to a textbook or even cite the relevant literature. This attempts to inflate the authors’ contributions in an effort to make them appear to be scientific. In 2.3 and 2.4, they then explained that a car on a beautiful summer day is hot inside, and a very long, complicated explanation of why this is so follows. Long explanations, pages without any reference to the actual topic, namely the greenhouse effect, but in which many of the same polemics against scholars such as Raschke are hidden. In 2.5 they add an experiment about a greenhouse made of potassium or sodium chloride instead of glass. This way visible and infrared light can pass the windows. This is to demonstrate that a greenhouse blocks the transport of heat by convection. This has no relation to the greenhouse effect in the atmosphere. All this would make sense for a polemic, or as a teaching example selected to explain the atmospheric greenhouse effect to students, but there is no connection to scientific work on the greenhouse effect. Putting everything together, again, the main message of Section 2 is that a greenhouse functions not by blocking infrared radiation, but by stopping turbulent heat convection. Since the atmospheric greenhouse effect is associated with the radiation budget of the earth, this whole discussion is irrelevant.

In Section 3, the authors search wide and far for a definition of the greenhouse effect. Section 3.2 is an overview of, no, not the scientific literature, but gray publications and press clippings from deniers and just about anything else from anyone anywhere. This is something I've never seen in a journal article. In 3.3 we find arbitrary statements of what the greenhouse effect is taken from anonymous sources found hither and yon (referred to as Anonymous 1, 2 and 3, completely untraceable. They could even have been invented by the authors) and a dictionary. It would be funny if it were not so sad. There are textbooks in which the greenhouse effect is explained precisely. One only needs to use them. This strange collection Gerlich & Tscheuschner can partly refute at least formalistically. But that is not relevant. This is yet another strawman attack, of which I have already described several.

Among the citations, for example, there is one correct description of the greenhouse effect issued in 1995 by the German Meteorological Society (GMS). The authors attempt to refute it. They attack, not the basic message of the statement, but claim that it confuses heat and thermal radiation (this is not the case). They try to convince us that the concept of a radiation budget is meaningless. That is nonsense and it is not justified by them in the slightest. They assume that radiation from the atmosphere is only emitted toward the ground. This is a straightforward barefaced lie, because the text of the GMS statement explicitly states that the radiation is emitted in all directions. This is a perfect example of the author’s approach. Such a thing should never get through peer review.

In another place, Rahmstorf’s explanation is ripped from its context in which he explains that atmosphere itself emits longwave radiation which thereby contributes to surface heating in addition to solar radiation thus warming the surface. The authors pretend that Rahmstorf had alleged that the greenhouse effect involves the reflection of radiation from the surface by the atmosphere. That is not what was written, and would of course be wrong. The authors then claim to have refuted Rahmstorf. Such reasoning might be suited to the beer cellar, the pub, the country club, or wherever you partake of your beverage of choice, but does not belong in a scientific journal.

Section 3.4, quotes from a report by the U.S. Department of Energy, that the designation "greenhouse effect" is misleading, because greenhouses do not work the same way as the atmospheric effect does. This does not prove what G & T assume it does, that there is no clear definition of the greenhouse effect and that it would be impossible to experimentally observe the greenhouse effect. Even worse, at this point, G & T claim that virtually no one can reproduce model calculations on the greenhouse effect. This statement is not substantiated. They try to make it appear as a quote, but the reference is only to the “Journal of Irreproducible Results”. Not an article in the journal, or an issue. The entire journal. Perhaps this was meant to be a "joke", but one that has never been seen in a serious article.

In another example, G & T quote elsewhere from an article by Bakan and Raschke in a booklet, in which the later correctly explained the greenhouse effect and also point out that the comparison with a real greenhouse is superficial. What prevented the authors from looking more closely at the literature they cite?

A biased overview of the history of the greenhouse effect

In Section 3.5 Gerlich and Tscheuschner then partially describe how Gore's popular-science lecture is wrong. For a scientific paper this is irrelevant and only polemical. For the most part, the section shows that reflection and the absorption / emission of radiation are different. That surprises no one. Again, it is simply irrelevant. Section 3.6, after a brief mention of the pioneering work of Tyndall and Fourier, shows why Arrhenius’ calculations were flawed. A century has passed since then, with higher-resolution spectra, much better models and better data on the composition of the atmosphere which all allow for improved calculations. The question arises about what is going on here, because it is well known that the Arrhenius’ calculations had problems, and they are now only of historical interest.

Obviously, this is just part of the polemic which extends throughout the paper: they search for examples of erroneous or incomplete explanations, and then refute, what no one wants to defend. An overview of modern work follows in the same section. There, however, the authors assemble a selective and misleading compilation, in order to give the appearance that model calculations predict everything and nothing. They make much of the fact that in a large set of calculation that overall predicted significant warming, there were a few that predicted cooling that were not featured. Throughout there are political shots directed at the green movement. In something published in 2009, one would hope that the IPCC Third and Fourth Assessment Reports would be accurately quoted, including their expectations for future increases in global temperature, but also the JASON, the Charney-and the Nierenberg Reports from 1979 and 1983 are missing. It is additionally striking that while the Third and Fourth Assessment Reports are actually cited in an entirely different place and not here where they should have been. It is obvious that the authors were not interested in providing a proper representation of current climate research.

Radiation Balance

In Section 3.7 on page 58 after interminable political polemics and irrelevant discussions of everything except the relevant science they finally begin dealing with the problem which is actually the basis of the greenhouse effect. First they claim that the concept of radiation balance is false because no law of conservation of intensity can be formulated. But that is irrelevant, because we can formulate a conservation law for the transferred energy. If one assumes a stationary case in which the energy of the Earth plus atmosphere remains constant a matching radiation budget can be built. Nothing else is behind the radiation balance diagrams. These are complete, because energy is conserved and therefore the amount of energy absorbed by and emitted from the earth must be equal and they are, as observed by measurements at least within their error limits. G & T deliberately misunderstand this, and then attempt to rebut what no one claims.

On page 61, using Equation 73, they derive the temperature of a planet without an atmosphere using radiation balance. Here, the radiation from the Earth is set equal to the solar radiation at the Earth, but the effect of the known albedo of the earth, 0.3, is described as being used to "tune" the equation although what this actually means is explained in all relevant textbooks. There is a confusing explanation of how the effective solar intensity striking the surface is reduced by the well-known factor of ¼, due to the fact that the sun shines on only one side of the Earth at a time and the angle at which the light strikes the surface outside of the equator. One has to look in the footnotes to find the explanation of what are described as tuning parameters in the text is really the measured albedo, and this is probably only there because of the repeated criticisms of this section which have appeared since 2007.

If the correct factors are used, one finds the known temperature of the earth without an atmosphere of 255 K. The authors then explain that the difference between this value and the observed temperature of the Earth's surface is the greenhouse effect. That is correct, only the authors falsely call this effect "fictitious". One has to remember that the back radiation from the atmosphere can be measured. Further satellites measure a mean radiation temperature of the atmosphere into space of about 255 Kelvin. It is obvious that the mean temperature of the earth's surface must be much higher, because otherwise it would be completely covered with ice. Institutions such as the Goddard Institute for Space Science and the Hadley Center, have determined the mean temperature of the earth's surface to be about 288 Kelvin. This temperature difference is practically a definition of the greenhouse effect on the basis of measurements and is misinterpreted by G & T.

Then the authors show that a derivation of the temperature of the earth gives different results when the earth is assumed to have a uniform temperature or a temperature distribution. A temperature distribution leads to a lower average temperature. This is also well known and trivial. In the extreme case of a planet that cannot rotate where the sun only shines on one side, the calculated temperature is very much lower than an Earth with a homogeneous temperature distribution. As with any idealization, the homogeneous surface temperature is not used in current models but only as an illustration, so this result is not relevant. It does not prove that there is no greenhouse effect, but only is a simplified model of providing a lower limit for the greenhouse effect. This is the exact opposite of what G & T wanted to prove.

Although G&T do not ever actually come to grips with a realistic model for the greenhouse effect, they then proclaim that they have falsified it. But they have only shown that a simplified model is a simplified model. That we knew.

G & T then show you cannot find a closed, exact solution for the radiation balance of a rotating Earth. That may be the case, but it is not a problem, because one can find numerical solutions for radiative transfer models with given boundary conditions and not that one has to calculate accurate surface temperature distributions from radiation balance condition.

They then refer to a publication of Schack in which the IR absorption of the atmosphere due to H2O and CO2, is calculated when the CO2 concentration rises. What this contributes is not clear. It furthers the polemics but does not contribute anything meaningful to understanding the greenhouse effect.

3.8 discusses heat conduction. It is irrelevant because heat conduction contributes little to energy distribution in the atmosphere which is primarily determined by radiation, latent heat and convection. Then in 3.9 the Laws of Thermodynamics are discussed. Behind this lurks the claim that the greenhouse effect requires heat transfer from the colder atmosphere to the warmer ground. This is not the case, rather the greenhouse effect requires a radiative interchange of heat between the atmosphere and the surface, in agreement with the Second Law, which also makes this point irrelevant. It is pathetic because of how quotes from Rahmstorf, among others, which explain the situation are deliberately misunderstood.

Attack on climate science in general

Section 4 carries the grandiloquent title "Physical fundamentals of climate science." Textbooks provide such things. The authors want to show that such fundamentals are not associated with the practice of climate science. Climate science is seemingly equated with climate models. Each climate model is based on a particular abstraction of nature with a matching set of physical, chemical, geological and biological equations. It is absurd, to try to make a single overarching statement about them. G & T quote, for example, criticisms of the models by the physicist Dyson which prove nothing or they cite a press release (!) of the British weather service, to present a counter position. They insinuate that climate models are not capable of adequately reliable statements about the future climate, because forecast models only give reliable predictions for a few days in the future {not in the IJMP version[JZ1]). I have already explained that this comparison is wrong: Weather forecasts are initial value problems, climate models solve boundary value problems, they have nothing to do with each other. G & T do not understand what they are reporting on here. Continuing, the authors make apparently scientific statements about the equations of fluid dynamics in order to show that models simplify nature too much to have any value. I have deliberately used such plain words - it is what is behind the statements of G & T's. Their statements are not provable and also nonsensical. Models are fundamental tools of science. Each model has a scope and associated uncertainties. Whether the results of the model are significant, must be determined in each case. Global judgments are nonsensical.

In 4.2 there is a long list of potentially relevant physical equations, without any demonstration of where and in what way they are relevant. Even worse equations appear that can be neglected in climate models, such as those for heat conduction, or such as Maxwell’s equations, that, to be sure are the basis of electromagnetic phenomenon, but without which one can describe the natural absorption and emission of radiation by greenhouse gases. Moreover, the basic equations are discretized in models (they are solved at grid points, in the atmosphere and the oceans), and as far as necessary, simplified. That is attacked without the authors demonstrating for even one model the extent to which these simplifications make the actual results for the given application useless. The criticism appears to be formally correct, but virtually has no substance and is irrelevant.

Section 4.3 is even worse, where the authors attempt to make a philosophical statement about what a scientific theory should look like, and, of course, "prove" that according to their statements in 4.2, climate models are not scientific. They falsely claim that the existence of a consensus in climate science is wrong and in any case was based on polls. Comically, the section ends with a polemic against the blog Real Climate.

Conclusion:

In summary, enormous time is taken to contradict what no one believes. G&T never attack the greenhouse effect which they don’t understand and don’t want to understand

What appears to be a scientific contribution hides a political polemic. Such things should not be published in any journal that wants to be recognized as serious. Something like this should not be published by anyone who wants to be accepted as a scientist. But unfortunately it has happened.

50 comments:

I know more than the average Joe about some of what he rants about. He is at my alma mater - the U of Ak Fairbanks, up on the West Ridge. He was a colleague of ex-professor, ex-researcher, and in many ways ex-scientist Syun-Ichi Sakasofu and sort of uses that as a bizarre club against other scientists and lay supporters of AGW (Obviously that's only one of his large array of tactics).

Akasofu's expertise is in high-energy atmospheric physics, and in particular the auroras. If the global warming debate was about HAARP, he'd be a world-class expert. He deservedly has a monument on campus. But he disgraced himself completely on the Great Global Warming Swindle, expounding on things that had nothing to do with AGW and attempting to conflate them with things that did, and chose to leave his career as a right-wing crank instead of a distinguished scientist.

I bring this up because the most glaring hole in Kramm's head is his repetition of the fact that Akasofu was a protege of Sidney Chapman, a very good space scientist, after whom our space science building is named. How dare you, he thunders, question a protege of Sidney Chapman on, well, anything??

Meanwhile, he is unceasing in his personal and professional attacks on James Hansen, who was a protege of James Van Allen!

Kramm is an educated fool for many reasons, but maybe the top one is, he doesn't even do ad authoritem arguments well.

From the discussion on PrimaKlima, Kramm doesn't seem to understand the math in my arXiv paper either, at least from his comments there (though my German is too poor to clearly follow what he's up to). He claims he found something wrong with one of the equations there? I'm pretty sure there were no typos or errors of that sort in any of the version I posted, but if there's a need for correction I'd love to hear it. His argument in the comments didn't make sense to me though - maybe somebody here can interpret?

Arthur, I presume, you mean this part. I hope, my English doesn't fail:

"The manuscript of Smith contains a few errors concerning the averaging. If you want to find the global average of a parameter, he following definition equation has to be used:y^M = INT_A_s(y dA_s)/INT_A_s dA_sHere A_s is the spheric angle (4 pi in case of a globe) and dA_s the differential spheric angle . y^M is the average over the globe for y. INT means integral. Contrary to eq. 6 by Smith the radius of the earth doesn't appear. When will you debunk the work by Smith?There is to mention, that the globally average temperature of the air near the surface (y=T) of about 288 K was calculated using the definition of a global average, too. This globally averaged temperature of the air near the surface has no connection with the temperature of 255 K, which is assumed to be homogeneous. "

Hmm, this is hardly an important point, since later on (like G&T) I assumed epsilon = 1 everywhere for the surface.

But Dr. Kramm, I have no idea what you mean by [eps]. I defined a quantity, eps_eff, in equation 8. Equation 9 is then a simple substitution using eq's 6 and 8, as can be easily seen by replacing the integral term in eq. 8 with E_emitted(t) divided by sigma (from eq. 6), and rearranging the terms.

I am german and I can promise you that Georg Hoffmann has nothing to say to the Gerlich @ Tscheuschner paper. He doesn't talk to Mr Kramm at all and is insulting everybody who doesn't believe in realclimatism.

Who are you to criticise Mr Kramm?

What is this joke all about? If there were a scientific debate, why is Mr Hoffmann so silent?

it is an important point. Not only is that a violation of basic rules of calculus, but it leads also to different results. However, this is not the real problem. We all make mistakes. This can only be avoided by doing nothing, and this is the biggest mistake.

The real problem is the style of scientific debates. To disagree with statements of the G & T paper is one thing, to initiate a cultural war is another one.

I took a look on various weblogs. It seems to me that a concerted action against the G & T paper has been installed. The publisher was bombarded with tons of e-mails. The journal IJMPB was put in the same corner like companies which make illegal copies of DVDs etc. (Take a look on Georg Hoffmann's weblog.) This is really sad.

I wonder why all these "experts" do not write comments to the G & T paper and submit it to the editor of the IJMPB. I promise you many of these "experts" will not do that because it is indispensable to use the correct name and affiliation. A comment, for instance, authored by the pseudonym "Eli Rabett" will not be accepted.

Commonly, comments to a paper submitted to the editor are given to reviewers and after they accept them to the authors. The authors have then the right to reply.

Scientific debates are very important. One of the finest hours of scientific debates can be related to the 5th Solvay Conference held in Brussels in 1927, when the giants of theoretical physics Albert Einstein, Niels Bohr and their pupils disputed quantum mechanics. When Einstein remarked "God does not play dice." Bohr replied, "Einstein, stop telling God what to do." This debate was a milestone in quantum mechanics. However, all participants did it under their own names, but not under pseudonyms. After this Solvey Conference quantum mechanics was more accepted as before. Even though Einstein was not entirely convinced he eventually recommended Werner Heisenberg for the Nobel-Prize in physics. That is greatness.

Equation (6) is important here, and Dr Kramm appears to follow that ok. It is an ordinary surface integral of the energy emitted from each point of the surface, using Stefan-Boltzmann law, to obtain the total energy emitted from the surface.

Equation (7) is a definition, for effective temperature T_eff. It uses another conventional surface integral to define a temperature value. Basically, it integrates fourth power of temperature over the surface, and then divides by total surface area.

Equation (8) is a definition also, for an effective emissitivity ε_eff. It uses same integral used in equation (6), and in order to relate the effective temperature to the total emitted energy..

Equation (9) is obtained by simple high school algebra. Just substitute in the definitions for T_eff and ε_eff, and you get equation 6 right back at you.

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So what's the problem? It's certainly not technical errors in Arthur's paper. Dr Kramm's comments on "solid angle" suggest he might merely be getting confused over co-ordinate systems. The equations (6) through (9) could be made more concrete in any co-ordinate system you like, such as latitude and longitude, in which case you could give the dx as a 4πr^2.dA, where dA is a small solid angle. But changing co-ordinate systems or variables is not a change to the equations, and Arthur properly uses the most general abstraction dx for a patch of area in a surface integral.

The equations given use local functions for temperature and emissivity, and they have two arguments: t, and x. These are not explicitly defined, but clearly t is time and x is location on the surface. Precisely what kind of co-ordinates are used for location is not important, any more than what units are used for the time.

Equation 6 is the total emitted radiant energy from a planet's surface. It's a really simple and basic formulation, and should be more than sufficient for someone to sort out the nature of variables used. Equation 6 simply adds up all the local bits of energy from each patch of surface area. It uses local emissivity and local temperature, for local energy, and integrates this over the planet's surface. The integral in equation 6 uses dx, which is clearly an area here, because x is a location on a surface. The units of the integration are therefore correct, because the Stefan Boltzmann law gives power per unit area.

Now; if you can figure that out, you just do precisely the same things with the definitions in Equations (7) and (8). They are just as mathematically meaningful. They are also physical sensible quantities. But to say the mathematics therein is nonsense is, well, nonsense!

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I totally reject the idea that anyone is immune from criticism by virtue of qualifications or standing. As it happens, I have a PhD in maths myself – although it is in discrete maths and graph theory rather than calculus. I've been involved in formal scientific/mathematical publishing, as author and as reviewer; although I have no particular prominence. I'm a very minor player. My own name is Chris Ho-Stuart, and am retired from academia and am no longer publishing.

The point is: it doesn’t matter. I don't care if you have the Field's medal or a Nobel prize; every statement or theorem or claim stands or falls on its own merits. Perhaps there's a language issue here with reading English, or perhaps it is a minor slip up; but Arthur's equations are good mathematical expressions of a basic surface integral.

Stick to the technical stuff. You've claimed a mathematical nonsense. I claim you're wrong, and the maths is trivially correct. I dismiss with contempt any attempt to bypass the specifics with grandstanding about standing.

If my explanation is any help and Dr Kramm retracts, then no harm done. It might just be a difficulty with language. Resolving such things is a win/win situation.

But if you still think the equations (7) to (9) are actually wrong or nonsensical, at least answer this: is equation (6) mathematically meaningful to you?

That is a total non-sequitur, of no relevance whatsoever to the point. Nothing in my comments, or in Arthur's equations, has anything involving equating a product of two integrals to a single integral. It's not just not there.

If you do this again, I'll get angry.

Answer the question, please. Does equation (6) make sense to you?

How would you calculate the total energy emitted from a surface, given functions for local temperature and emissivity?

Arthur's equations involve simple surface integrals, which are correct not only for a sphere but any radiating object.

Dr. Kramm, you have not shown anywhere that the equations in question logically lead to an equation where the product of two integrals is equal to the integral of the product. It is just not in there.

In one comment here you rearrange equation 8 as:

eps_eff T^4_eff = C INT (eps T^4) dx

C = 1/(4 pi r^2)

However, this is still not the product of two integrals, because the definition of eps_eff includes T_eff^4 (defined by an integral) in the denominator and you are left with a tautology. As is obvious given that (7) and (8) are merely definitions of T_eff and eps_eff, respectively.

Physically, equation 8 defines an "effective" emissivity by weighting the local emissivity by the fourth power of local temperature. A perfectly natural thing to do.

I see Arthur has made a short comment going to the heart of Dr Kramm's errors. But as I had prepared this longer reply, I'll post also. Dr Kramm has a succession of comments here.

(A) Integral of a product

Dr Kramm has made some remarks about integrals of a product (in a comment at 9:03pm), but they are irrelevant. Neither Arthur nor I have ever equated the integral of a product with a product of the integrals. Continued invocation of this point is an irrelevant distraction. It indicates that Dr Kramm is very sloppy in looking the equations he presumed to criticize.

I can only guess that Dr Kramm noticed two integrals that do appear within these equations: In equation (6) and (8), there is a reference to INT ( ε(t,x) T(t,x)^4 dx). In equation (7) there is a reference to INT ( T(x,t)^4 dx ). But nowhere is there an integral of ε(t,x) by itself.

It appears that Dr Kramm has merely jumped to the conclusion, on the basis of nothing at all, that there must be a distribution of an integral across a product somewhere. But there isn't. Dr Kramm frankly ought to apologise for this distraction and for the dig about reading text books.

(B) Re-arranging equation (8)

In a comment at 9:08pm, Dr Kramm speaks of a rearrangement of equation 8.

In his comment, Dr Kramm states that this equation 8 can be simply rearrange to give this:eps_eff T^4_eff = C INT (eps T^4) dxwhere C is 1/(4πr^2)

Then Dr Kramm states that this is a nonsense. But it isn't a nonsense at all. The claim that this simple rearrangement is "nonsense" drops out of thin air with no basis at all.

This equation is being used to define the quantity eps_eff, and this rearranged formulae is a perfectly proper way to express the definition. The eps inside the integral is the given local eps, which is defined over different locations. Equation 8 proposes a definition for a global effective emissivity. It's a perfectly good mathematical definition, with no mathematical errors. The number obtained is a sensible way of representing a kind of effective global emissivity. It's not an "average", but an "effective" emissivity.

(C) Integrating over a sphere

Dr Kramm states that equation 6 is nonsense because

[y] = 1/(4 pi) INT_A_s y dA_s

is the proper way to integrate over a sphere. But this is just a co-ordinate issue. It's a particular case of the more general surface integral, where you integrate over areas.

The equation Arthur has used is the more general surface integral, which applies to any surface. The Earth, in fact, is NOT a sphere. You can handle that in polar co-ordinates, or in any co-ordinates you like, but ultimately the check for whether you are integrating correctly is whether or not you are doing INT(y dx) where dx is a small surface area.

Dr Kramm states that the radius of a sphere plays no role in this integral. That should make him think twice! Recall, we want to calculate the total energy being emitted from the Earth. Stephan Boltzmann gives you energy per unit area. So you have to multiply it by an area to get an energy.

In a conventional surface integral, as used by Arthur, the dx is an area; we integrate over many small patches of area. If there is a co-ordinate transform of some kind so that you can integrate over the solid angle in a sphere, then you'll find the radius of the sphere has to go into the function y, as part of the change of variable operation… and you are no longer integrating simply a Stephan-Boltzmann term for power per unit area!

If Dr Kramm would just think for a minute, he'd surely recognize that ANY calculation of the total energy emitted by a sphere at a certain temperature is going to use the radius of the sphere somewhere! If he thinks about where it goes, he'll get precisely what I explained in the first place. It's just a basic co-ordinate transform, and the "dx" area has to be replaced by 4πr^2.dA where dA now has units of solid angle.

To say that one of these alternatives is "wrong" while the other is "right" is… well, words fail me.

----

The major point that strikes me is that this is all so very elementary. If Dr Kramm applied a bit of simple algebra to the equations he presumes to criticize, then he'd see that the remarks about product of integrals were irrelevant.

If Dr Kramm actually carried through a calculation of total energy with his preferred solid angle method, he would see the radius of a sphere appearing inside the integral, in precisely the form needed to make dA into a small patch of area as used in the more conventional surface integrals by Dr Smith, using dx.

And finally, the bland claim, based on nothing at all that I can see, of equation 8 being "mathematical nonsense", is surreal. This is a definition, which should be considered on its physical merits -- which are pretty obvious. Its mathematical standing is fine. Dr Kramm has no meaningful mathematical objections at all.

I'm not satisfied with my remarks on surface integrals, and I'll try to say it again more clearly. Sorry for the extra space...

If you want to integrate some quantity over the surface of a sphere, you do a surface integral. Suppose, for example, we want to know how much water there is in the ocean. We can integrate the depth of the ocean over the surface area. So let D(x) be the depth in a given area x.

In full generality, the surface integral is INT( D(x) dx ) where dx represents a small patch of area.

You can convert units, by expressing a small area dx = 4πr^2 dA, where dA is a small solid angle, and r is the radius of the earth. The integral becomes INT (D(A) 4πr^2 dA). For a sphere, r is constant, and you can bring it out of the integral to get 4πr^2 INT (D(A) dA).

For an ellipsoid planet, however, that would be an error. In general, r may be a function of the part of the surface being considered. On Earth, for example, the equatorial radius is about a third of a percent larger than the polar radius. In general, r is a function of A, and you can't just bring it out of the integral as you can for a sphere.

In either case, however, the integral must still be equivalent to INT ( D(x) dx ). It's just a transformation of variables, and to single out solid angle as the only way to write a surface integral over a sphere is just ignorant.

In a general discussion of temperature and emissivity, the best method is the most general method, where you keep explicit that it is a surface integral over small patches of surface area. It's completely accurate, it is simpler to express, and it is fully general.

It seems to me that a concerted action against the G & T paper has been installed. The publisher was bombarded with tons of e-mails.

That's because all those people were amazed and upset that a blatant work of pseudoscientific idiocy got published in a real journal, even if a minor one. It's rather as if a paper by creationists had been published in a biology journal.

Duae - thanks - so does anybody want to translate this explanation of Kramm's errors into German to respond on the PrimaKlima thread? Or maybe somebody already pointed out his nonsense there? The discussion there has overwhelmed my limited German, I'm afraid!

Interesting that the publishers were overwhelmed with emails about this paper. I'm glad people actually care, that's encouraging.

By your logic, the definition of eps_eff would require substitution of eps for T everywhere in equation 7, which would NOT lead to:

eps_eff(t) = 1/(4 pi r^2) INT (eps(x, t) dx)

but rather would lead to:

eps_eff(t)^4 = 1/(4 pi r^2) INT (eps(x, t)^4 dx)

which is a completely different equation anyway.

But I meant, and wrote, neither of those things to define eps_eff. I wrote equation 8 to define eps_eff. That is the definition. I'm sorry that this has confused you, but it seems not to have confused any of the dozens of others who have read the paper.

I think this all boils down to Dr. Kramm reading "an effective emissivity [...] can be defined as an average over the planetary surface" as "an effective emissivity [...] can be defined as unweighted average of the emissivity over the planetary surface". Dr. Kramm, please correct me, if I should be wrong with the above.

I do not agree with the above reading, because: A) The sentence in question starts out with "Similar to the effective albedo", which is not a simple average either.B) The sentence leads up to equations (7) and (8), where T_eff and eps_eff are explicitly defined.

I do not see, how one can construe that Arthur Smith intended to use or actually did use the unweighted average of the emissivity in equation (9), when he clearly took care to define an effective emissivity, which clearly is the correct choice in equation (9).

In the 11th comment at 8:42 pm, Dr Kramm responds to my detailed explanations by saying that I must believe integration distributes over multiplication, and makes a rather belittling remark about needing to look at textbooks on calculus. He's repeated the insinuation several times subsequently.

Now in fact, there is absolutely nowhere in any of my work or Arthur's paper where an integration is distributed over a product as he implies. It is simply not there. A high school student could see this.

I can accept a slip up. With a decent and honest person, when this is pointed out they will apologize, and acknowledge that they were wrong to make the accusation, and progress is made. That I even need to ask this is telling. My normal expectation with anyone having a bare minimum of competence and decency is that they would recognize they had slipped up, acknowledge it, and we could move on.

I will, sometime soon, be addressing the various other claims by Dr Kramm, but I am choosing to single out this one issue as a point where I want to see if progress is possible. Whatever else we address, please take up this one.

You explicitly accused me of thinking integration distributes over a product. I don't mind in the least if someone points out when I make a stupid error in calculations – but if the mistake isn't there, I expect them to recognize the error and retract the insinuation. If you can't even do that, how can we hope to progress on anything?

The only mistake I made is that I wrote in some of my remarks Eq. (6) of Smith. It must read Eq. (7).

Arthur,

with your Eq. (7) you defined what an effective quantity does mean. It is an average over the surface of the entire globe.

Consequently, the quantity eps T^4 under the integral of the right-hand side of Eq. (8) has to be treated in the same manner. This means that your Eq. (8) has to be written

{eps T^4}_eff = C INT (eps T^4) dx

with

C = 1/(4 pi r^2). The left-hand side of this equation is the effective emitted energy normalized by the Stefan constant.

If you consider your Eq. (8) as the definition of eps_eff, then your eps_eff diagrees with the definition of an effective quantity as the average over a sphere. It is an attempt to compare apples with pears.

In turbulence there is a similar problem: Let the braces [ ] define the averaging integral. The average of a product a b is then given by

[a b] = [a] [b] + [a' b']

In accord with your Eq. (8) It would mean that

[a] = [a b]/[b]

However, the correct one is

[a] = ([a b] - [a' b'])/[b]

Since the covariance term [a' b'] is not generally equal to zero, your mathematical treatment is not self-consistent.

Dr Kramm. You explicitly accused me of thinking integration distributes over multiplication! Here is what you said previously.

Quoting Dr Kramm: "obviously, you are believing that

INT (f(x) g(x) dx) = INT (f(x)dx) times INT (g(x)dx)

is correct. Please take a sharp look into textbooks on calculus."

That is a specific claim of a specific and very silly error in my calculations. If I do ever make such a silly mistake, I'll have no problem with you pointing it out and I'll thank you for the correction sincerely. Anyone can make silly mistakes.

But if YOU are incorrect to claim I have been distributing integration over a product, then elementary decency means you acknowledge it and retract your claim about my making this mistake.

Is this hard to understand? Deal with the question. I insist that you either retract this claim, or else repeat it.

We'll get onto the other stuff, but your integrity is on the line here. Anyone can make a dumb mistake from time to time. All it takes is simple high school algebra to see that there's no distribution of integration over a product here. And you should own up to that, and admit you were wrong to suggest I've done any such thing.

This is an error, by you, and you should admit it.

If you have the elementary decency and competence to manage that, then there may be some hope for progress as I move on to the other points.

Gerhard Kramm said: "It seems to me that a concerted action against the G & T paper has been installed. The publisher was bombarded with tons of e-mails. The journal IJMPB was put in the same corner like companies which make illegal copies of DVDs etc."

As one of the people who wrote an e-mail to the editors, I would like to say that I have absolutely no regrets about such action. It is simply inexcusable that the editors of a serious scientific journal publish a piece of polemical nonsense that launches utterly fallacious attacks on a whole field of science and is called a "review article". If they can't find a competent reviewer then they shouldn't publish it...In fact, it should have been clear simply from the tone of the article that it was unpublishable as is, let alone the mistakes one finds once one subjects it to any real scientific review.

Gerhard Kramm says: "I wonder why all these 'experts' do not write comments to the G & T paper and submit it to the editor of the IJMPB. I promise you many of these 'experts' will not do that because it is indispensable to use the correct name and affiliation. A comment, for instance, authored by the pseudonym 'Eli Rabett' will not be accepted."

Many of us here, including myself and Arthur Smith, are using our names and I am sure others would be willing to in appropriate circumstances. As for submitting a comment or a paper in response, that is something that we have been working on collaboratively here. However, since it is very time-consuming to do this, since the nature of G&T writing is so obtuse that it is difficult to pin them down exactly on what they are saying (for example, please give me a clear statement of EXACTLY why the believe the atmospheric greenhouse effect violates the 2nd Law of Thermodynamics), and since there is little reward to be earned by rebutting something that almost all serious scientists know is just garbage, this is a pretty thankless task.

For the record, I also sent a brief and polite email to the journal, in my own name, suggesting that their normal processes for quality control and review are broken. I was advised to submit any corrections as a paper to the journal.

I have subsequently made some contributions to the response being worked on here, which might or might not go to IJMP(B); in which case I again use my own name.

However, in my opinion, it is simply not appropriate to carry on a debate over undergraduate level physics and high school level maths in a professional journal. If there is a need to do that, then the journal has failed its proper role.

The fact is, in this instance the editors failed the journal, and published a blatant bit of outright crackpottery, riddled with trivial errors. This happens occasionally, and in an ideal world the journal itself takes note of how it occurred and cleans up their procedures.

If there are editors who actually need to have formal submissions to see such fundamental problems, then they are completely useless as editors of a professional journal. Hopefully someone at IJMP is doing something about this and cleaning house a bit. But that's up to them.

In the meantime, I don't mind trying to explain matter in a forum like these comments, but there's no way this kind of discussion should appear in a professional journal. We have some people claiming that there are trivial errors in calculus, and others claiming that the calculus is 100% correct. Some people are claiming that a certain physical model violates fundamental laws of thermodynamics, while others say that the model is perfectly consistent with thermodynamics and indeed a consequence of thermodynamics.

This is not a debate appropriate to a credible journal! It might be needed, but if so that is a damning indictment on the journal.

If I may make a meta-comment here, it seems to me that Dr. Kramm is using a rhetorical technique rather similar to that of G&T themselves. What it seems to amount to is this: One takes something and then finds an interpretation of it (sometimes quite convoluted) and then says that because one has come up with an interpretation of it where it does not make sense, therefore it is nonsense.

Of course, the correct way to read a scientific paper is to understand what the author actually meant by what he said and to see if it makes sense under that interpretation. Admittedly, if you think that what the author meant from what he said is sufficiently unclear, one would note that the paper has a pedagogical issue but one would not conclude that it is nonsense. (The fact that most of us reading Arthur's paper didn't seem to have any significant trouble interpreting what he said makes it unclear whether there is even any potential pedagogical issue here.)

In relating this to G&T, I think it is instructive to compare, say, their section where they complain about various statements of the greenhouse effect with this website: http://www.ems.psu.edu/~fraser/BadMeteorology.html Fraser is quite a stickler for pedagogy and, in fact, he is a bit too militant about pedagogy for my tastes. However, the important thing is that when he comes across a statement about the greenhouse effect that he objects to, he makes a complaint about the pedagogy and does not jump to the conclusion that the whole of the science is nonsense. Apparently, there are people in this world who are missing the ability to make this distinction (or, if one wants to be more cynical about motives, which I would like to avoid but find hard to sometimes, who are purposely confusing the issues to obfuscate rather than illuminate).

By contrast, in our discussions of the G&T paper, we have labored quite hard to understand what they are saying...but can't find any way to make what they say make sense. Hence, there are some of us who think that G&T are wrong because they didn't realize that the fact that the atmosphere can warm the earth's surface more than its absence does not imply that the NET flow of heat is still from earth to atmosphere. There are others of us who believe they just didn't understand that one can only apply the Clausius statement to the NET heat flow. However, regardless of how we interpret what G&T are saying, we cannot come up with a interpretation in which their claim that the greenhouse effect violates the 2nd Law is correct.

Hmmm...my phrase "does not imply that the NET flow of heat is still from earth to atmosphere" in the previous post seems to have either too few or too many not's in it, depending on your point of view.

Perhaps the best fix is to replace "imply" with "contradict the fact".

You know, sometimes there is just no there there. Gerlich, Tscheuschner and Kramm are simply clueless. Undergraduates who never came to a lecture, never cracked a book and sailed through on aggression and attitude because it was easier to walk away from them then deal with the nonsense.

So Dr. Kramm, please tell us how all those radiometers that have measured emission from the atmosphere to the ground are doing criminal physics, or is there some majic shield on the surface that prevents the radiated energy from being absorbed.

Undergraduates who never came to a lecture, never cracked a book and sailed through on aggression and attitude because it was easier to walk away from them then deal with the nonsense."

Reminds me of some other nonsense in the news these days: the economic nonsense of Alan Greenspan, Larry Summers, Robert Rubin, Tim Geithner, et al.

The above description fits these folks to a T. For example, Greenspan, Summers and Rubin were quite insistent (to the point of bullying) that a woman named Brooksley Born was wrong when she warned that unregulated derivatives could bring our banking system and economy crashing down. Born persisted in her warnings to no effect -- because pretty much everyone else backed off and she was cut off at the pass by the bullies.

Of course, Born was right and the Bullies were dead wrong.

But the Bullies nonetheless won the day and the American people lost (big time) because, as we all know, bullies have big egos, big mouths and even bigger sticks (metaphorically speaking, of course).

The Bullies NEVER back off themselves but have to be forced out -- as Summers was finally forced out of the Harvard Presidency by the words and actions of folks who are MUCH smarter an much more cunning than he is.

The Bullies are attracted to bureaucratic positions like a moth toward the flame, since that's the one place where they can get away with their badgering.

Unfortunately, the Bullies (Summers, Geithner and others) are back in the saddle in the Obama administration.

My equation 7 defines, as the text explicitly states, a quantity T_eff. This is *not* the average value of the temperature T - that is why I called it an "effective radiative temperature", and not the "average temperature". Similarly, equation 8 *defines* an "effective emissivity". The very brief sentence before 7 and 8 explains that these quantities *can be defined* by the following equations. Now I did use the word "averages over the planetary surface", but these obviously weighted averages - the effective temperature is weighted by the fourth power of itself, and the effective emissivity is weighted by the forth power of local temperature.

The paper later goes on to discuss actual averages, as in equation 11, which defines T_ave.

The primary object of this entire first section of the paper is the inequality of equation 12, which relates that actual average temperature T_ave, to the weighted averages T_eff, eps_eff and a_eff, in the case of a planet with no atmosphere.

Why do you insist that eps_eff is an unweighted average of the emissivity, when I make no such claim? It is, as you point out, mathematically incorrect to use the unweighted average. *That is why I did not use it!*

It SHOULD be pretty clear to anyone who reads further than number 8 -- and especially to those of us who get as far as number 12 -- that you are drawing a distinction between "effective" and (simple) "average".

How someone who has a PhD in meteorology and teaches atmospheric science at the university level (even as an associate faculty member) could fail to grasp that is really hard to fathom.

in fact, i don't buy that kramm does not understand.

I have to agree with Joel's assessment above. it's the only possibility that makes any logical sense.

..which means that trying to further clarify it to Kramm is a waste of time (yours).

I think you are assuming that Kramm honestly believes you are mistaken.

Given that Kramm is actually "arguing" about are essentially definitions (eg, of effective emissivity), that assumption is really hard to swallow.

He understands all right. That's almost certainly not the issue here.

Not sure whether that's the issue with T&G. They may actually believe that there is no atmospheric greenhouse effect, kind of like the guy who sits pertrified wondering when he will fall through the spaces between the atoms in his chair. I suspect that he's not subject to logic either.

Here, A is the surface of the sphere, A_s is the solid angle (A_s = 4 pi in the case of a sphere), dA_s is the differential solid angle, and r is the radius of the sphere. There is no other way to define a reasonable surface average. Obviously, the radius plays no role.

If we set Y = T^4, then the planetary average is given by

[T^4] = 1/(4 pi) INT_A_s (T^4 dA_s)

It is clear that [T^4] is not equal to (T_eff)^4.

In the case of Y = eps, the planetary average reads

[eps] = 1/(4 pi) INT_A_s (eps dA_s)

This means that Smith's eps_eff given by his Eq. (8) is not a planetary average as he stated before.

Arthur,

please, do not try to correct Gerlich and Tscheuschner with wrong or inappropriate equations.

Gerhard Kramm

P.S.: In my manuscript on Smith's averaging procedures (see http://www.gi.alaska.edu/~kramm/climate/Arthur%20Smith%20and%20the%20basic%20rules%20of%20calculus.pdf ), one can find a more detailed explanation.

If you find Arthur's terminology confusing, I suggest that you replace the word "averages" with "appropriately-weighted averages". However, I have to admit that I am puzzled as to why a little ambiguity in terminology has thrown you off so much. Clearly there are different sorts of averages and Arthur's equations define the sort of averages that he has found it useful to define. You seem to be the only one who was so hopelessly confused by this point.

And, Gerlich and Tscheuschner seem to be the only ones who were so hopelessly confused by the different statements in the literature regarding the atmospheric greenhouse effect that they came to the ridiculous conclusion that it violates the Second Law of Thermodynamics.

And, frankly, I find myself confused about whether it is really possible for PhD physicists and meteorologists to get so easily confused by minor issues of terminology and definitions or whether there is actually a purposeful attempt at obfuscation going on. Or, maybe it is just a shining example of people not understanding what they do not want to understand. I don't know.

Smith's equations speak for themselves. The way he has DEFINED effective emissivity is perfectly reasonable and in line with how it is normally defined in the literature.

If you can't see this, it's not Smith's fault -- and certainly not something he should even concern himself about.

For such a trivial case, words are only necessary for the non-mathematically inclined.

If you indeed don't understand this (and are among the non-mathematically inclined), the ones who should really be concerned are your colleagues at the U of Alaska. (Just my opinion, of course)

But I think that you do understand it and quite frankly find it absolutely pathetic that you would resort to a petty rhetorical "argument" over terminology rather than admit you are wrong in this case.

Since I am well familiar with density-weighted averages (see, e.g., Kramm and Meixner, 2000, Tellus 52A, 500-522), I immediately checked, whether Smith's "average" is in substantial agreement with a weighted average. It is not.

Dear Anonymous (7:26)

please list textbooks or papers in which Smith's averaging procedure used in his Eqs. (7) and (8) is defined. I would like to laugh.

For convenience we can use square brackets to represent a simple surface average. If V(x) is some variable that has different values in different regions, then the average may be denoted [V], which is a single value for the whole surface.

This is defined by a surface integral. [V] = INT(V(x) dx) / Area.

In the special case of a sphere you can do a substitution of variables, so as to integrate over solid angles, rather than over small areas directly, if you really want. The substitution is dx = r^2 dA, where dA is a small solid angle and r is the sphere's radius. For a sphere, you getINT(V(x) dx) / Area = INT(V(A) r^2 dA) / 4.pi.r^2 = INT(V(A) dA) / 4.pi[V] = INT(V(A) dA) / 4.pi

The two formulations are exactly the same, as long as you have a sphere. Arthur's paper uses the more general formulation, which is better because the Earth is not quite a perfect sphere.

Every time you see Dr Kramm insisting that the only way to handle this integration is with solid angles rather than with areas, or every time you see him say that the "radius" should or shouldn't appear in some formulae, you are seeing him make this mistake in elementary calculus – an inability to do a simple change of variable.

A weighted average is simply [V.w]/[w], or [V.w/[w]], since [w] is a constant value that does not depend on the part of the surface. The expression w is the weight. What you use for a weight depends on the application.

Using this notation, the equations in Arthur's paper could be given as follows. (7) Τ_eff ^4 = [T^4] -- defines T_eff using an unweighted average of T^4(8) e_eff = [ε.T^4] / T_eff^4 -- defines e_eff as a ratio of unweighted averages.That is, the effective emissivity is simply defined to be that which gives you the average energy when applied to the average temperature^4 using Stefan-Boltzmann.

You can also think of e_eff as a weighted average. It's not "density" weighted, of course, unless you use density as a synonym for weight; it's weighted by T^4.e_eff = [ε.T^4] / T_eff^4 = [ε.Τ^4]/[Τ^4]... and that is what a weighted average means.

Nothing shows up better how completely confused Dr Kramm is that he actually wants a text book for this. Whether this is deliberate malice in attempt to confuse readers, or whether Dr Kramm is actually this incompetent, I cannot judge. Which ever it is, it won't help to hold his hand through simple text book definitions and try to teaching him how to apply them in reading a real paper. The explanations given here will be enough for anyone with minimal ability. If these explanations are not enough, a text book won't help either.

Like I said before, what both Dr. Kramm and G&T are doing is nitpicking pedagogy but pretending that this then leads to something that is incorrect by deliberately refusing to understand what the author meant. I.e., they work their hardest to come up with convoluted interpretations different from what they authors meant under which they can argue that what is written does not make sense. This is completely against the spirit of scientific inquiry. It is perhaps what a lawyer would do if he had to defend a client who was so obviously guilty that he didn't have any serious arguments that he could make.

The only people who don't see through this sort of deceitfulness (or extreme self-delusion) are those who want to be fooled, but I suppose that is the whole point: Now, those on the internet who want to believe that Arthur's critique of G&T is wrong will be able to point to Dr. Kramm's nonsense to convince themselves and their compatriots to continue to believe real scientific nonsense.

"The two formulations are exactly the same, as long as you have a sphere. Arthur's paper uses the more general formulation, which is better because the Earth is not quite a perfect sphere."

Smith only considered a sphere because its surface is 4 pi r^2. If one considers the true shape of the earth because the radius of the equator, 6378.14 km, is larger than the radius to the poles, 6356.75 km, owing to centrifugal forces, one has to write for the average over the earth's surface (using your notation):

Ah, but in the case where the planet is not a sphere, one simply has to take 'r' as the "effective" radius of the planet, and the formula works just fine :-)

Duae, your explanation of why I used the word "average" in the text above and what I meant by equations 7 and 8 is spot on. I might even update the arXiv paper to clarify this a bit better (but then, what would the Kramm's of the world find to complain about? Ah, of course, he still has his solid angle argument to go on).

I did have a few other typos and corrections I've been collecting so now might be a good time to send in an update. Probably not this week though.

is correct. It's what you have to do when "r" is a function of "A", rather than constant everywhere. The best method, however, is to keep it as simple as possible and use dx = r^2 dA with a simple change of variable to integrate over area directly. That gives:

[V] = INT(V dx) / Area

which is the more fundamental definition of an average over any surface. It avoids an completely irrelevant distraction about "r".

But look! Kramm has just implicitly acknowledged he's been wrong to insist the radius plays no role. For example, see his comment above at 9:17 PM a few days back. Back then he gives an expression than is only strictly correct when "r" is a constant.

[V] = INT(V dA) / 4pi

Kramm has been saying that the more general surface integral dx is "wrong". He's got enough knowledge to understand that he should retract that objection. The reason he's not given the retraction yet is apparently not simply incompetance, but a lack of integrity.

This argument about how to do an average over a surface is really a side (freak?) show to the main event.

Lots of scientists (eg, at NASA and elsewhere) have done that and the answer always comes out close to 288K. This is not rocket science. It's a very simple surface integral that pretty much anyone who has had basic calculus can do, at least to get a ballpark figure, which indeed DOES come out close to 288K.

The fact is, Kramm can't argue against the greenhouse effect -- because that requires a denial of reality.

So he argues about whether an average taken over a surface has to have an "r-squared" appearing explicitly in the formula (or not).

it's absurd.

Apparently no one ever informed Kramm that spherical coordinates are not the only (and not even the most general) coordinate system you can use for the earth.

------- Quote -------"[Yet, be that what it may, Gerlich and Tscheuschner have found a physics journal to house their contribution. It is the International Journal of Modern Physics, B, not a journal of geophysics, climatology or meteorology but a journal that publishes articles about condensed matter, high temperature superconductors, and statistical and applied physics. To attentive observers this immediately raises red flags that something is seriously wrong. You would not expect editors of such a journal to have much expertise about climate. According to the published rules of the journal all review articles, such as that of Gerlich and Tscheuschner must be invited which is still more concerning]"------- End Quote -------

You're obviously a fish in a small pond. You think that all you need is to be an expert in climatology in order to understand climate science.

There are lots of climate data analysis tasks that obviously you don't need to be an expert in climatology in order to conduct an analysis.

First, in science (whatever disciplines), you can analysis the data via using axiomatic-driven models (ie, physical processes as in physics/climate models are fully/partially known in advance as apriori) where expertise in this area are definitely needed. Second case, if one doesn't know the underlying processes in advance (apriori), then one has to revert to data-driven models in order to estimate or make rough guesses about those unknown underlying processes. This means that you don't need to be an expert at all in climate science, the only requirement is that one needs to understand the particular data-driven methods being used and that's fact.

I can quote you some examples of climate science data analytics that were published in non-related climate journals, such as computing, data-mining, etc,... If those papers were to submit to a climate related journal, I bet that reviewers from those journals (would have no clue to the methods/algorithms being used in those papers because those methods/algorithms are still unknown to climate scientists). Here are some examples:

There are tons that I can quoted, but the 3 references that I have linked to above clarifies my point. Your criticism of the reviewers for International Journal of Modern Physics is at best unscientific.

Eli thinks it good that anyone writing on climate understand basic thermo. Other than that a passing acquaintance with the data and the basics helps a heap.

Unfortunately G&T have none of the above

With regard to your three papers it would be a good thing if at least one of the authors understood how the data series they are cranking on was constructed.

Eli just picked the second one at random on downscaling, and the authors include people who work on hydrology, so yeah, since they work on hydrology, publish in the Journal of Hydrology, it is dollars to donuts that the editor can find referees, especially since journals always ask you to propose a couple of referees.

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Eli Rabett

Eli Rabett is a not quite failed professorial techno-bunny, a chair election from retirement, at a wanna be research university that has a lot to be proud of but has swallowed the Kool-Aid. The students are naive but great and the administrators vary day-to-day between homicidal and delusional. His colleagues are smart, but they have a curious inability to see the holes that they dig for themselves. Prof. Rabett is thankful that they occasionally heed his pointing out the implications of the various enthusiasms that rattle around the department and school. Ms. Rabett is thankful that Prof. Rabett occasionally heeds her pointing out that he is nuts.